耦合強度與居量相關聯之安德森模型的熱力學特性分析

Thermodynamic Properties of the Anderson Model with Correlated Hybridization

王鐘漢(Chung-han Wang)

指導教授 ： 郭光宇

國立臺灣大學/理學院/物理研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.01452

摘要

近藤效應於1930年左右被觀察到後，為了成功解釋這現象，許許多多的理論以及計算方式如雨後春筍的冒出，數值重整化群(numerical renormalization group)就是其中之一，這個方法厲害之處在於不會像是其他的計算方式在低溫處失效，是第一個能成功計算至超低溫的方法。
本論文一開始會先介紹近藤效應，並於第二章介紹了數值重整化群以及計算熱物理量的方法。在第三章之中嘗試利用數值重整化群計算材料La(1-x)Ce(x)Al(2)，此材料由於具有4f軌域的電子，且此4f軌域電子即為形成近藤效應的關鍵，所以一直以來都是研究近藤效應的好材料，而在模擬的過程中發現了其中雜質的能階以及雜質電子與傳導電子間的耦合強度的決定並不容易，所以討論這兩個物理量對整個系統的影響就是第四章的主軸，在第四章之中將會改變系統的耦合強度以及雜質能階，並計算其雜質所貢獻的比熱與熵還有磁化率。
而在第五章中我們討論了耦合強度與居量相關安德森模型，也就是耦合強度將不再是個常數，而會隨著系統居量而改變，並了解做了這個改變後對於系統的影響。

關鍵字

近藤效應 ； 數值重整化群 ； 安德森模型

並列摘要

After the discovery of the Kondo effect by De Haas in the 1930’s lots of theoretical and numerical methods were developed. For example Numerical Renormalization Group method. This method is a noteworthy development as unlike other techniques it does not breakdown when applied to low energy scale calculations.
This thesis will begin with a brief introduction to the Kondo effect. After this brief summary, chapter 2 will introduce what the Numerical Renormalization Group method is.
There are numerous rare-earth metallic compounds with atomic have f orbitals and the wide s-d band coexist at the Fermi level. These have a variety of unique thermal and magnetic properties. These rare-earth metallic compounds can be described by the Anderson Model, so I try to use the Numerical Renormalization Group method to calculate the properties of the La(1-x)Ce(x)Al(2).system in chapter 3
To understand the behavior of the impurity and the influence of different hybridization strengths and impurity energy with regards to the Kondo effect, the Numerical Renormalization Group method will be used to calculate the thermal dynamics of the Anderson model like entropy and specific heat in chapter 4.
At chapter 4 we sets the hybridization strength to be a constant. In chapter 5 we use the Correlated Hybridization Anderson model to consider the effects on the system of changing the hybrization strength to now be depended on impurity occupation number. Any changes to the system are then assessed

並列關鍵字

Kondo effect ； Numerical Renormalization Group ； Anderson model

參考文獻

1. de Haas, W.J., J. de Boer, and G.J. van den Berg, The electrical resistance of gold, copper and lead at low temperatures. Physica, 1934. 1(7–12): p. 1115-1124.

2. Kondo, J., Resistance Minimum in Dilute Magnetic Alloys. Progress of Theoretical Physics, 1964. 32(1): p. 37.

3. Sarachik, M.P., E. Corenzwit, and L.D. Longinotti, Resistivity of Mo-Nb and Mo-Re Alloys Containing 1% Fe. Physical Review, 1964. 135(4A): p. A1041-A1045.

4. Anderson, P.W., Localized Magnetic States in Metals. Physical Review, 1961. 124(1): p. 41-53.

5. Goldhaber-Gordon, D., et al., From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor. Physical Review Letters, 1998. 81(23): p. 5225-5228.